1. Field of the Invention
The present invention is directed to a method for determining optimized radio-frequency pulse shapes for selective excitation of an examination subject in magnetic resonance spectroscopy and imaging.
2. Description of the Prior Art
In both in magnetic resonance spectroscopy and imaging, each nuclear magnetic resonance data-acquiring event is preceded by excitation of the examination subject with a radio-frequency (RF) pulse, having a frequency coinciding with the Larmor frequency. When the examination subject is subjected to a magnetic field gradient G.sub.z in the presence of such a radio-frequency pulse, in addition to being subjected to the uniform basic field B.sub.0, the resonant frequency .omega..sub.R varies according to the formula EQU .omega..sub.R =.gamma.(B.sub.0 +G.sub.z .multidot.z)
along the examination subject, wherein .gamma. is the gyromagnetic constant and z is the locus coordinate along the z-axis.
Only nuclei in a layer having the position EQU z=(.omega..sub.R -.gamma.B.sub.0)/.gamma.G.sub.z
are forced out of equilibrium. Only these nuclei contribute nuclear magnetic resonance signal, while all other nuclei remain uninfluenced. Such radio-frequency pulses are referred to as "selective". Such pulses are employed in magnetic resonance spectroscopy in order to obtain spectra from localized regions of the examination subject. For imaging purposes, it is similarly only one layer of the examination subject which is excited with a selective radio-frequency pulse in virtually all instances, and a two-dimensional or three-dimensional resolution within this layer is implemented in the following read-out sequence using phase and frequency coding.
A typical spin-echo sequence is shown in FIGS. 1 through 4 as a example of the use of selective radio-frequency pulses. FIG. 1 shows two radio-frequency pulses RF1 and RF2 and the resulting signal S. FIGS. 2, 3 and 4 respective show the curves for the slice selection gradient G.sub.S, the phase-coding gradient G.sub.P, and the read-out gradient G.sub.R.
In the spin echo sequence, a selective 90.degree. radio-frequency pulse RF1 is first generated in the presence of a slice selection gradient G.sub.S. Subsequently, the direction of the slice selection gradient G.sub.S is inverted, and a phase-coding gradient G.sub.P is generated. The FID signal which is excited as a result, however, is not directly read out. Instead, a spin echo signal S, which is read out under a read-out gradient G.sub.R is obtained by generating a second selective radio-frequency pulse RF2 having a flip angle of 180.degree..
The illustrated sequence is multiply repeated with different values of the phase-coding gradient G.sub.P. The signal S is measured for each value of the phase-coding gradient G.sub.P, and these corresponding signal values are entered into a row of a measurement matrix. Using two-dimensional Fourier transformation, an image of the spin density in the examined layer can be produced.
In the illustrated sequence, two slice-selective radio-frequency pulses RF1 and RF2 are generated, with the pulse RF1 serving the purpose of excitation and the pulse RF2 producing a spin echo.
Methods for nuclear magnetic resonance imaging are explained in greater detail in the article "NMR Imaging Techniques and Applications: A Review", Bottomley, Review of Scientific Instrumentation, Vol. 53, No. 9, September 1982. The illustrated spin echo sequence merely represents an example of a large number of instances in nuclear magnetic resonance technology wherein selective radio-frequency pulses are employed.
The goal in the selective excitation of a slice is to generate a slice profile, i.e., the size of the flip angle which is actually achieved, in a rectangular coordinate system wherein the other axis is the locus axis. Fashioning of a selective radio frequency pulse which meets this demand is difficult because a nuclear spin system does not react linearly to a radio frequency excitation. The system can be considered linear only for small flip angles (&lt;30.degree.), because the Block equations, which describe the reaction of the spin system to radio-frequency pulses, are approximately linear only in that range. The excitation spectrum would have to be rectangular given for a perfectly linear system. This can be achieved by modulating the radio-frequency signal with a sinc function sin x/x. For larger flip angles such as, for example, 90.degree. or even 180.degree., however, the sinc function no longer leads to satisfactory slice profiles. Inadequate slice profiles lead to poor T1 and T2 tissue contrasts in gradient echo and spin echo images because of the non-uniform flip angle distribution across the selected slice. It is also a disadvantage that the signal intensity varies across the slice. On the basis of numerical solutions, those in this field have attempted to fashion selective radio-frequency pulses which improve the slice profile. Such attempted solutions are described, for example, in "Parameter Relations for Shinnar-Le Roux Selective Excitation Pulse Design Algorithm" Pouly et al., IEEE Transactions on Medical Imaging, Vol. 10, No. 1, March 1991. Such numerical methods, however, are complex and do not always lead to satisfactory solutions.